fit.egp {mev}

Parameter stability plot and maximum likelihood routine for extended GP models

Description

The function tstab.egp provides classical threshold stability plot for (\kappa, \sigma, \xi). The fitted parameter values are displayed with pointwise normal 95% confidence intervals. The function returns an invisible list with parameter estimates and standard errors, and p-values for the Wald test that \kappa=1. The plot is for the modified scale (as in the generalised Pareto model) and as such it is possible that the modified scale be negative. tstab.egp can also be used to fit the model to multiple thresholds.

Usage

fit.egp(xdat, thresh, model = c("egp1", "egp2", "egp3"), init, show = FALSE)

tstab.egp(
  xdat,
  thresh,
  model = c("egp1", "egp2", "egp3"),
  plots = 1:3,
  umin,
  umax,
  nint,
  changepar = TRUE,
  ...
)

Arguments

xdat

vector of observations, greater than the threshold

thresh

threshold value

model

a string indicating which extended family to fit

init

vector of initial values, with \log(\kappa) and \log(\sigma); can be omitted.

show

logical; if TRUE, print the results of the optimization

plots

vector of integers specifying which parameter stability to plot (if any); passing NA results in no plots

umin

optional minimum value considered for threshold (if thresh is not provided)

umax

optional maximum value considered for threshold (if thresh is not provided)

nint

optional integer number specifying the number of thresholds to test.

changepar

logical; if TRUE, the graphical parameters (via a call to par) are modified.

...

additional arguments for the plot function, currently ignored

Details

fit.egp is a numerical optimization routine to fit the extended generalised Pareto models of Papastathopoulos and Tawn (2013), using maximum likelihood estimation.

Value

fit.egp outputs the list returned by optim, which contains the parameter values, the hessian and in addition the standard errors

tstab.egp returns a plot(s) of the parameters fit over the range of provided thresholds, with pointwise normal confidence intervals; the function also returns an invisible list containing notably the matrix of point estimates (par) and standard errors (se).

Author(s)

Leo Belzile

References

Papastathopoulos, I. and J. Tawn (2013). Extended generalised Pareto models for tail estimation, Journal of Statistical Planning and Inference 143(3), 131–143.

Examples

xdat <- mev::rgp(
  n = 100,
  loc = 0,
  scale = 1,
  shape = 0.5)
fitted <- fit.egp(
  xdat = xdat,
  thresh = 1,
  model = "egp2",
  show = TRUE)
thresh <- mev::qgp(seq(0.1, 0.5, by = 0.05), 0, 1, 0.5)
tstab.egp(
   xdat = xdat,
   thresh = thresh,
   model = "egp2",
   plots = 1:3)